Mumbai university sent a letter to Kajal stating that the scholarship amount has been accepted and credited to her account. Will this amount be considered as a part of National income?

No, it will not be considered

Only those transactions which have a corresponding flow of goods and services are included while calculating the national income. As, this is a transfer payment which is unilateral in nature, thus, it will not be included in the calculations. Various transfer payments include: old age pension, unemployment allowances, scholarships to students, charity etc.